Paramagnetic Spin-orbit Terms Research Articles

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy.

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

NMR spin–spin coupling constants in microhydrated ortho-aminobenzoic acid

The influence of the hydrogen-bond formation on the NMR spin–spin coupling constants, including the Fermi contact, the diamagnetic spin–orbit, the paramagnetic spin–orbit and the spin dipole term, has been investigated for the ortho-aminobenzoic acid microhydrated with up to three water molecules. The one-bond and two-bond spin–spin coupling constants for several intra-molecular and across-the-hydrogen-bond atomic pairs are calculated employing high-level density functional theory in combination with the B3LYP functional with two different types of extended basis sets for each level of microhydration. The spin–spin coupling constants, in general, vary inversely with the hydrogen bond length. The Fermi contact term is found to be the dominant contributor to the total value of spin–spin coupling constant followed by the paramagnetic spin–orbit term. The variations of Fermi contact term and atomic charge distribution with size of microhydration follow quite similar trend. The effect of explicit solvation provided by microhydration has also been compared briefly with that of bulk implicit solvation obtained through polarised continuum model and mixed microhydration/continuum approach.

Critical analysis of the through‐space transmission of NMR JFH spin–spin coupling constants

AbstractNMR JFH coupling constants transmitted through space are known to show several unusual peculiarities. The main three are (a) in many cases their experimental values are reported to be positive and in others, negative; (b) theoretical values show that in some cases they are substantially contributed not only from the Fermi contact (FC) term but also from the paramagnetic spin orbit (PSO) term, and their respective signs could be either like or unlike; (c) in many cases it can hardly be expected that the corresponding FH proximate interactions could be considered a “hydrogen bond,” whereas in other cases it is evident that they are. For discussing points (a) and (b), characteristics of both the FC and PSO terms are discussed performing qualitative analyses based on their expressions given in terms of the polarization propagator formalism. Point (c) is discussed in terms of the well‐known Bader's QTAIM method as well as recalling the known relationship between the transmissions of the Fermi hole and of the FC interaction of spin–spin coupling constants. © 2012 Wiley Periodicals, Inc.

Effect of Electronic Interactions on NMR 1JCF and 2JCF Couplings in cis- and trans-4-t-Butyl-2-fluorocyclohexanones and Their Alcohol Derivatives

In order to study the influence of hyperconjugative, inductive, steric, and hydrogen-bond interactions on (1)J(CF) and (2)J(CF) NMR spin-spin coupling constants (SSCCs), they were measured in cis- and trans-4-t-butyl-2-fluorocyclohexanones and their alcohol derivatives. The four isotropic terms of those SSCCs, Fermi contact (FC), spin dipolar (SD), paramagnetic spin-orbit (PSO), and diamagnetic spin-orbit (DSO), were calculated at the SOPPA(CCSD)/EPR-III level. Significant changes in FC and PSO terms along that series of compounds were rationalized in terms of their transmission mechanisms by employing a qualitative analysis of their expressions in terms of the polarization propagator formalism. The PSO term is found to be sensitive to proximate interactions like steric compression and hydrogen bonding; we describe how it could be used to gauge such interactions. The FC term of (2)J(CF) SSCC in cis-4-t-butyl-2-fluorocyclohexanone is rationalized as transmitted in part by the superposition of the F and O electronic clouds.

Probing 1J(C−F) and nJ(F−F) Spin−Spin Coupling Constants for Fluoroazines: An Ab Initio Theoretical Investigation

Ab initio equation-of-motion coupled cluster singles and doubles calculations have been carried out to evaluate one-bond C-F coupling constants (1)J(C-F) and three-, four-, and five-bond F-F coupling constants (n)J(F-F) for a series of mono-, di-, and trifluoroazines. The computed (1)J(C-F) and (n)J(F-F) values for these are in good agreement with available experimental coupling constants. The values of (1)J(C-F) vary as the number and positions of N atoms and the number and relative positions of C-F bonds change, but it is difficult to discern general patterns for these changes due to opposing effects of the Fermi contact and paramagnetic spin-orbit terms. The majority of (1)J(C-F) values lie in a range that includes the three monosubstituted pyridines. For trifluoroazines, (1)J(C-F) for a C-F bond that is ortho to two other C-F bonds is greater than (1)J(C-F) for the other two bonds. F-F coupling constants arise in these molecules when the two C-F bonds are ortho, meta, or para. Values of (3)J(F-F) are relatively large and negative, whereas values of (5)J(F-F) are relatively large and positive. (4)J(F-F) may be positive or negative and large or small. The value of this coupling constant depends on the nature of the atom that links the two C-F bonds and the number and positions of N atoms in the ring. The calculations carried out in this study at a reliable level of theory give values for one-bond C-F and n-bond F-F spin-spin coupling constants for the fluoroazines that are not available experimentally. In addition, the patterns that describe the changes that occur in these molecules provide a basis for predicting their values in larger, related systems in the absence of experimental data and direct calculations.

Benzylic coupling constants in toluene derivatives by J doubling in the frequency domain and DFT calculations

The recently modified J doubling in the frequency domain method (MJDFDM) allowed the determination of (4, 5, 6)J(H, CH(3) ) in toluene, a series of 4-mono- and 3,5-disubstituted toluene derivatives, as well as in 4-picoline. The methyl and aromatic signals were subjected to successive deconvolution processes, which at the end led to singlet signals and afforded the corresponding coupling constant values with a high degree of accuracy. Density functional theory calculation of benzylic coupling constants by addition of the Fermi contact, the spin-dipole, the diamagnetic spin-orbit, and the paramagnetic spin-orbit terms revealed good agreement between predicted and measured values when the B3LYP/aug-cc-pVTZ level of theory was used. Evaluation of the substituent effect over the coupling constant was made for all studied compounds and some limitations of the methodology were evidenced.

Analysis of One-Bond Se-Se Nuclear Couplings in Diselenides and 1,2-Diselenoles on the Basis of Molecular Orbital Theory: Torsional Angular Dependence, Electron Density Influence, and Origin inJ1(Se, Se)

Nuclear couplings for the Se-Se bonds, 1 J(Se, Se), are analyzed on the basis of the molecular orbital (MO) theory. The values are calculated by employing the triple ζ basis sets of the Slater type at the DFT level. 1 J(Se, Se) are calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence on ϕ(CMeSeSeCMe). The dependence explains well the observed 1 J obsd (Se, Se) of small values (≤ 64 Hz) for RSeSeR′ (1) (simple derivatives of 1a) and large values (330–380 Hz) observed for 4-substituted naphto[1,8-c, d]-1,2-diselenoles (2) which correspond to symperiplanar diselenides. 1 J (Se, Se: 2) becomes larger as the electron density on Se increases. The paramagnetic spin-orbit terms contribute predominantly. The contributions are evaluated separately from each MO (ψ i) and each ψ i → ψ a transition, where ψ i and ψ a are occupied and unoccupied MO's, respectively. The separate evaluation enables us to recognize and visualize the origin and the mechanism of the couplings.

Torsional Angular Dependence of 1J(Se,Se) and Fermi Contact Control of 4J(Se,Se): Analysis of nJ(Se,Se) (n=1–4) Based on Molecular Orbital Theory

(n)J(Se,Se) (n=1-4) nuclear couplings between Se atoms were analyzed by using molecular orbital (MO) theory as the first step to investigating the nature of bonded and nonbonded (n)J(Se,Se) interactions between Se atoms. The values were calculated by employing Slater-type triple xi basis sets at the DFT level, which were applied to structures optimized with the Gaussian 03 program. The contribution from each occupied MO (psi(i)) and psi(i)-->psi(a) (psi(a)=unoccupied MO) transition was evaluated separately. 1J(Se,Se) was calculated for the MeSeSeMe model compound, which showed a typical dependence on the torsion angle (phi(C(Me)SeSeC(Me))). This dependence explains the small values (< or =64 Hz) of 1Jobsd(Se,Se) observed for RSeSeR' and large values (330-380 Hz) of 1Jobsd(Se,Se) observed for 4-substituted naphtho[1,8-c,d]-1,2-diselenoles, which correspond to synperiplanar diselenides. The HOMO-->LUMO and HOMO-1-->LUMO transitions contribute the most to 1J(Se,Se) at phi=0 and 180 degrees to give large values of 1J(Se,Se), whereas various transitions contribute and cancel each other out at phi=90 degrees to give small values of 1J(Se,Se). Large 4Jobsd(Se,Se) values were also observed in the nonbonded Se...Se, Se...Se=O, and O=Se...Se=O interactions at naphthalene 1,8-positions. The Fermi contact (FC) term contributes significantly to 4J(Se,Se), whereas the paramagnetic spin-orbit (PSO) term contributes significantly to 1J(Se,Se). 2J(Se,Se) and 3J(Se,Se) were analyzed in a similar manner and a torsional angular dependence was confirmed for 3J(Se,Se). Depending on the structure, the main contribution to (n)J(Se,Se) (n=2, 3) is from the FC term, with a lesser contribution from the PSO term. Analysis of each transition enabled us to identify and clearly visualize the origin and mechanism of the couplings.

19F– 19F and 19F– 1H spin–spin coupling constants in cyclic FH polymers (FH) n, n=2–6

Spin–spin coupling constants 2h J(F–F), 1 J(F–H), and 1h J(H–F) have been obtained for cyclic complexes (FH) n , with n=2–6, from ab initio equation-of-motion coupled cluster singles and doubles (EOM-CCSD) calculations. Although both the Fermi-contact (FC) term and 2h J(F–F) increase and become positive as the cluster size increases, the FC term is not a good quantitative approximation to 2h J(F–F). The paramagnetic spin–orbit (PSO) and spin–dipole (SD) terms which contribute to 2h J(F–F) appear to be sensitive to the orientation of the hydrogen-bonded pair. However, the large increase in the FC term and 2h J(F–F) as the size of the cluster increases is due primarily to the reorganization of σ electron densities in both ground and excited states, and is another manifestation of cooperativity effects in hydrogen-bonded cyclic polymers. The FC term and 1 J(F–H) always increase upon complex formation, but 1 J(F–H) increases only slightly as the size of the cluster increases due to a concurrent decrease in the PSO term. The changes in 1 J(F–H) as a function of polymer size reflect the polarization of electron density away from H and toward F in the ground state, and the electron reorganization which occurs in the excited states which couple to the ground states through the FC and PSO operators. The FC term is a good approximation to 1h J(H–F), and is always negative, indicating that the hydrogen bonds in the FH clusters are traditional hydrogen bonds.

Elucidation of the Electronic Structure of Molecules with the Help of NMR Spin−Spin Coupling Constants: The FH Molecule

It is demonstrated how the one-bond NMR spin-spin coupling constant (SSCC) (1)J(FH) can be used as a source of information on the electronic structure of the FH molecule. For this purpose, the best possible agreement between measured and calculated SSCC is achieved by large basis set coupled perturbed density functional theory calculations. Then, the calculated value is dissected into its four Ramsey terms: Fermi contact, the paramagnetic spin-orbit term, the diamagnetic spin-orbit term, and the spin dipole term, which in turn are decomposed into orbital contributions and then described by their spin densities and orbital current densities. In this way, the SSCC gives detailed information about the electronegativity of F, the bond polarity, the bond polarizability, the volume and the polarizability of sigma and pi lone pair orbitals, the s- or p-character of the bond orbital, the nature of the LUMO, and the density distribution around F.

Investigation of the π Character of a C−C Bond with the Help of the Diamagnetic and Paramagnetic Spin−Orbit Term of the NMR Spin−Spin Coupling Constant

The NMR spin-spin coupling constant (SSCC) 1 J(C-C) is a sensitive antenna for investigating the electronic structure in hyper- and π-conjugated hydrocarbons. The magnetic dipole field of the perturbed nucleus generates orbital currents, which are experienced by the responding nucleus, thus leading to the paramagnetic spin-orbit (PSO) coupling mechanism. The strength of the orbital currents depends on the availability of high-lying occupied and low-lying virtual orbitals with distinct p π or p σ character, the nodal properties of these orbitals, and the overlap between zeroth- and first-order orbitals. For C-C bonds in unsaturated hydrocarbons, the value of 1 PSO(C-C) depends on opposing effects such as the p σ and the p π character of the C-C bond (i.e., the degree of hybridization at the C atoms and the degree of π delocalization in the conjugated system). This dependence leads to the overall cubic behavior of the PSO term when given as a function of the C-C bond character and the strong scattering of PSO values for a given bond type. Under certain conditions, the degree of hybridization can be determined with the help of the PSO term. Also, the PSO term helps to distinguish hyperconjugation and π-conjugation effects. For a given C-C bond type with fixed or similar hybridization at the C atoms, the PSO term can be given as a function of the C-C bond order, thus representing a sensitive descriptor for the degree of π delocalization.

Analysis of the paramagnetic spin–orbit transmission mechanism for NMR spin–spin coupling constants using the paramagnetic spin–orbit density distribution

For the analysis of the paramagnetic spin orbit (PSO) term of the NMR spin–spin coupling constant (SSCC), ring current density and PSO density distribution are derived and used to explain magnitude and sign of the isotropic PSO term. Decomposition of the PSO components into orbital contributions helps to identify those orbital pairs (occupied, virtual) dominating the PSO term. The induction of strong ring currents requires low excitation energies and complementing nodal properties of zeroth and first order orbitals. The PSO components for a typical triple, double, and single CC bond are explained.

DFT study of the NMR properties of xenon in covalent compounds and van der waals complexes-implications for the use of 129Xe as a molecular probe.

The NMR properties (chemical shift and spin-spin coupling constants) of (129)Xe in covalent compounds and weakly bound complexes have been investigated by DFT methods including relativistic effects. For covalent species, a good agreement between experimental and calculated results is achieved without scalar relativistic effects, but their inclusion (with a triple-zeta, double-polarization basis set) leads to some improvement in the quality of the correlation. The spin-orbit coupling term has a significant effect on the shielding constant, but makes a small contribution to the chemical shift. Coupling constants contain substantial contributions from the Fermi contact and paramagnetic spin-orbit terms; unlike light nuclei the spin-dipole term is also large, whereas the diamagnetic spin-orbit term is negligible. For van der Waals dimers, the dependence of the xenon chemical shift and anisotropy is calculated as a function of the distance. Small (<1 Hz) but non-negligible through-space coupling constants between (129)Xe and (13)C or (1)H are predicted. Much larger couplings, of the order of few Hz, are calculated between xenon and (17)O in a model silicate residue.

Interpretation of indirect nuclear spin-spin coupling tensors for polyatomic xenon fluorides and group 17 fluorides: results from relativistic density-functional calculations.

Significant improvements have been made recently in the calculation of NMR indirect nuclear spin-spin coupling tensors (J). In particular, the relativistic zeroth-order regular approximation density-functional theory (ZORA-DFT) approach holds great promise for the calculation of spin-spin coupling constants for a variety of chemical systems containing heavy nuclei. In the present work, the ZORA-DFT method is applied to the calculation of the complete reduced coupling tensors, K, for a range of chlorine-, bromine-, iodine-, and xenon-containing species: K(Cl,F) for ClF(2)(+), ClF(3), ClF(4)(+), ClF(5), ClF(6)(-), and ClF(6)(+); K(Br,F) for BrF(3), BrF(6)(-), and BrF(6)(+); K(I,F) for IF(4)(+) and IF(6)(+); K(Xe,F) for XeF(+), XeF(2), XeF(3)(+), XeF(4), XeF(5)(-), XeF(5)(+), and XeF(7)(+). These species represent a wide variety of geometrical bonding arrangements. Agreement between the calculated coupling constants and available experimental data is excellent, and the absolute sign of the coupling constants is provided. It is shown that (1)K(iso) may be positive or negative even within the same molecule, e.g., K(Cl,F)(iso) may be of either sign, depending on the local environment. Periodic trends in (1)K(iso) for isovalent and isostructural molecules are evident. The spin-spin coupling anisotropies, Delta K, and the orientations of the K tensors are also determined. The success of the calculations is a direct result of employing reliable geometries and considering both scalar and spin-orbit relativistic effects. The dependence of K(Cl,F)(iso) and K(Xe,F)(iso) on the local molecular and electronic structure is discussed in terms of the paramagnetic spin-orbit (PSO) and combined Fermi-contact spin-dipolar (FC+SD) coupling mechanisms. The PSO term depends strongly on the number of valence shell electron lone pairs on the central heavy atom, and the FC+SD contribution increases with the Cl[bond]F or Xe[bond]F bond length for a given series of compounds. This interpretation allows for the successful rationalization of the existing experimental data.

Periodic trends in indirect nuclear spin-spin coupling tensors: relativistic density functional calculations for interhalogen diatomics.

There have been significant advances in the calculation and interpretation of indirect nuclear spin-spin coupling (J) tensors during the past few years; however, much work remains to be done, especially for molecules containing heavy atoms where relativistic effects may play an important role. Many J tensors cannot be explained based solely on a nonrelativistic Fermi-contact mechanism. In the present work, the relativistic zeroth-order regular approximation density-functional (ZORA-DFT) implementation for the calculation of J has been applied to the complete series of homonuclear and heteronuclear diatomic halogen molecules: F(2), Cl(2), Br(2), I(2), At(2), ClF, BrF, IF, ClBr, ClI, and BrI. For all of these compounds, the reduced isotropic coupling constant (K(iso)) is positive and the reduced anisotropic coupling constant (DeltaK) is negative. With the exception of molecular fluorine, the magnitudes of K(iso) and DeltaK are shown to increase linearly with the product of the atomic numbers of the coupled nuclei. ZORA-DFT calculations of J for F(2) and ClF are in excellent agreement with the results obtained from multiconfigurational self-consistent-field calculations. The relative importance of the various coupling mechanisms is approximately constant for all of the compounds, with the paramagnetic spin-orbit term being the dominant contributor to K(iso), at approximately 70-80%. Available experimental stimulated resonant Raman spectroscopy data are exploited to extract the complete J((127)I,(127)I) tensor for iodine in two rotational states. The dependence of K(iso) and DeltaK on bond length and rovibrational state is investigated by using calculated results in combination with available experimental data. In addition to providing new insights into periodic trends for J coupling tensors, this work further demonstrates the utility of the ZORA-DFT method and emphasizes the necessity of spin-orbit relativistic corrections for J calculations involving heavy nuclei.

A density functional study of nuclear magnetic resonance spin–spin coupling constants in transition-metal systems

We report the first extensive DFT-based study of the one-bond metal-ligand nuclear spin-spin coupling constant 1 K(M, X). Calculations are presented on 1 K(M, X) in 3d-, 4d- and 5d-transition-metal carbonyl, oxo, fluoro, and phosphine complexes of affordable size for which experimental coupling constants are available. An analysis based on molecular orbitals makes it possible to identify all key contributions to the Fermi-contact (FC) coupling term and rationalize the periodic trends in the coupling constants. Based on this analysis, it is shown that the FC coupling contribution is a valence property with core orbitals playing only a minor, indirect role. Through a similar analysis it is concluded that lone pair orbitals hardly contribute to the paramagnetic spin–orbit (PSO) coupling term. The study also examines the validity of the finite perturbation method (for the FC term) and the uncoupled perturbation method (for the PSO term). The results from frozen-core calculations in 3d- and 4d-complexes are mostly in good agreement with experimental data. The quasirelativistic correction on top of the frozen-core treatment gives a significant but insufficient improvement for the coupling constants in 5d-complexes. The impact of relativity on the size of 1 K(M, X) is discussed and it is suggested that relativistic schemes more sophisticated than the simple quasirelativistic approach are needed for 5d-elements.